Sequence and floor function
Source: Romania TST 1990
August 6, 2009
functioninductionalgebra unsolvedalgebra
Problem Statement
The sequence is defined by:
x_1\equal{}1
x_{n\plus{}1}\equal{}\frac{x_n}{n}\plus{}\frac{n}{x_n}
Prove that increases and [x_n^2]\equal{}n.